1. Among 150 math students 42 have taken Discrete Math, 32 have taken History of

Question

1. Among 150 math students 42 have taken Discrete Math, 32 have taken History of Math. There are 10
have taken both.
(a.) How many students have taken only Discrete Math, but not History of Math?
(b.) How many students have taken only History of Math, but not Discrete Math?
(c.) How many students have taken only one of Discrete Math or History of Math?
(d.) How many students have taken neither course?
(e.) How many stuents have taken at least one of Discrete Math or History of Math (possibly both)?

Explanation / Answer

N(S) = 150
N(D) = 42
N(H)= 32
N(H INTERSECT M) =10

a)-> students have taken only Discrete Math, but not History of Math= 42- 10 = 32

b)- students have taken only History of Math, but not Discrete Math= 32 -10 = 22

c)- students have taken only one of Discrete Math or History of Math= 32 +22 = 54

d)- students have taken neither course= 150 -( 32 +10 + 22) = 86

e)- students have taken at least one of Discrete Math or History of Math = 32 + 10 + 22 = 64

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